References
- Biazar , J. 2010 . Analytic solution for telegraph equation by differential transform . Phys. Lett. A , 374 : 2904 – 2906 . (doi:10.1016/j.physleta.2010.05.012)
- Chen , J. , Liu , F. and Anhb , V. 2008 . Analytical solution for the time-fractional telegraph equation by the method of separating variables . J. Math. Anal. Appl. , 338 : 1364 – 1377 . (doi:10.1016/j.jmaa.2007.06.023)
- Ciment , M. and Leventhal , S. H. 1975 . Higher order compact implicit schemes for the wave equation . Math. Comput. , 29 : 985 – 994 . (doi:10.1090/S0025-5718-1975-0416049-2)
- Dai , W. Z. and Nassar , R. 2000 . A compact finite difference scheme for solving a three-dimensional heat transport equation in a thin film . Numer. Methods Partial Differential Equations , 16 : 441 – 458 . (doi:10.1002/1098-2426(200009)16:5<441::AID-NUM3>3.0.CO;2-0)
- Dai , W. Z. and Nassar , R. 2002 . An unconditionally stable finite difference scheme for solving a 3D heat transport equation in a sub-microscale thin film . J. Comput. Appl. Math. , 145 : 247 – 260 . (doi:10.1016/S0377-0427(01)00579-9)
- Dehghan , M. and Ghesmati , A. 2010 . Combination of meshless local weak and strong (MLWS) forms to solve the two dimensional hyperbolic telegraph equation . Eng. Anal. Bound. Elem. , 34 : 324 – 336 . (doi:10.1016/j.enganabound.2009.10.010)
- Dehghan , M. and Mohebbi , A. 2009 . High order implicit collocation method for the solution of two-dimensional linear hyperbolic equation . Numer. Methods Partial Differential Equations , 25 : 232 – 243 . (doi:10.1002/num.20341)
- Dehghan , M. and Shokri , A. 2008 . A numerical method for solving the hyperbolic telegraph equation . Numer. Methods Partial Differential Equations , 24 : 1080 – 1093 . (doi:10.1002/num.20306)
- Deng , D. W. and Zhang , Z. Y. 2008 . A new high-order algorithm for a class of nonlinear evolution equation . J. Phys. A: Math. Theor. , 41 p. 015202.
- Ding , H. F. and Zhang , Y. X. 2009 . A new fourth-order compact finite difference scheme for the two-dimensional second-order hyperbolic equation . J. Comput. Appl. Math. , 230 : 626 – 632 . (doi:10.1016/j.cam.2009.01.001)
- Evans , D. J. and Bulut , H. 2003 . The numerical solution of the telegraph equation by the alternating group explicit (AGE) method . Int. J. Comput. Math. , 80 : 1289 – 1297 . (doi:10.1080/0020716031000112312)
- Gao , Z. and Xie , S. S. 2011 . Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional schrödinger equations . Appl. Numer. Math. , 61 : 593 – 614 . (doi:10.1016/j.apnum.2010.12.004)
- Geiser , J. 2008 . Fourth-order splitting methods for time-dependant differential equations . Numer. Math. Theory Methods Appl. , 1 : 321 – 339 .
- Jordan , P. M. and Puri , A. 1999 . Digital signal propagation in dispersive media . J. Appl. Phys. , 85 : 1273 – 1282 . (doi:10.1063/1.369258)
- Jordan , P. M. , Meyer , M. R. and Puri , A. 2000 . Causal implications of viscous damping in compressible fluid flows . Phys. Rev. E , 62 : 7918 – 7926 . (doi:10.1103/PhysRevE.62.7918)
- Karaa , S. 2010 . Unconditionally stable ADI scheme of high-order for linear hyperbolic equations . Int. J. Comput. Math. , 87 : 3030 – 3038 . (doi:10.1080/00207160902878548)
- Liao , H. L. and Sun , Z. Z. 2011 . Maximum norm error estimates of efficient difference schemes for second-order wave equations . J. Comput. Appl. Math. , 235 : 2217 – 2233 . (doi:10.1016/j.cam.2010.10.019)
- Liu , J. M. and Tang , K. M. 2010 . A new unconditionally stable ADI compact scheme for the two-space-dimensional linear hyperbolic equation . Int. J. Comput. Math. , 87 : 2259 – 2267 . (doi:10.1080/00207160802624133)
- Mickens , R. E. and Jordan , P. M. 2004 . A positivity-preserving non-standard finite difference scheme for the damped wave equation . Numer. Methods Partial Differential Equations , 20 : 639 – 649 . (doi:10.1002/num.20003)
- Mohanty , R. K. 2009 . New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations . Int. J. Comput. Math. , 86 : 2061 – 2071 . (doi:10.1080/00207160801965271)
- Mohanty , R. K. and Jain , M. K. 2001 . An unconditionally stable alternating direction implicit scheme for the two space dimensional linear hyperbolic equation . Numer. Methods Partial Differential Equations , 17 : 684 – 688 . (doi:10.1002/num.1034)
- Mohanty , R. K. , Jain , M. K. and Arora , U. 2002 . An unconditionally stable ADI method for the linear hyperbolic equation in three space dimensions . Int. J. Comput. Math. , 79 : 133 – 142 . (doi:10.1080/00207160211918)
- Orsingher , E. 1986 . A planar random motion governed by the two-dimensional telegraph equation . J. Appl. Probab. , 23 : 385 – 397 . (doi:10.2307/3214181)
- Rashidinia , J. , Mohammadi , R. and Jalilian , R. 2007 . Spline methods for the solution of hyperbolic equation with variable coefficients . Numer. Methods Partial Differential Equations , 23 : 1411 – 1419 . (doi:10.1002/num.20229)
- Sun , H. L. , Qin , M. Z. , Wang , Y. S. and Scherer , R. 2010 . Multi-symplectic Birkhoffian structure for PDEs with dissipation terms . Phys. Lett. A , 374 : 2410 – 2416 . (doi:10.1016/j.physleta.2010.04.011)
- Thomas , J. W. 1995 . Numerical Partial Differential Equations: Finite Difference Methods , New York : Springer-Verlag . Texts in Applied Mathematics 22
- Uzezi , E. S. and Shariffudin , R. H. 2011 . Armadillo generation distributed system with geranium Cadcam cluster for solving 2D telegraphic problem . Int. Comput. Math. , 88 : 589 – 609 . (doi:10.1080/00207161003633162)
- Yıldırım , A. 2010 . He's homotopy perturbation method for solving the space- and time-fractional telegraph equations . Int. Comput. Math. , 87 : 2998 – 3006 . (doi:10.1080/00207160902874653)
- Yousefi , S. A. 2010 . Legendre multiwavelet Galerkin method for solving the hyperbolic telegraph equation . Numer. Methods Partial Differential Equations , 26 : 535 – 543 .